Are there any problems which can be solved by human brain in a very less time but a computer may take a lot of time or a computer could never solve it ?
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7$\begingroup$ Is your question about the current state-of-the-art in computers or their theoretical limitations? $\endgroup$– usulCommented Feb 18, 2013 at 16:23
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1$\begingroup$ Parsing natrual language. $\endgroup$– mrkCommented Feb 18, 2013 at 23:11
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5 Answers
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The now standard simple example of this is CAPTCHAs which stands for "Completely Automated Public Turing test to tell Computers and Humans Apart" which was intentionally devised in the theoretical community partly to detect and deflect automated spammers. However, the technology can be subverted somewhat by some systems such as mechanical turk. The term "CAPTCHA" was coined in 2000 by Luis von Ahn, Manuel Blum, Nicholas J. Hopper, and John Langford (all of Carnegie Mellon University). CAPTCHAs have gotten increasingly visually complex over the years as computer algorithms for character recognition have improved, in other words its evolving and something of a red queen race, i.e. evolutionary "arms race".
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Language processing.
Every kid learns how to use language within his first 1-3 years. Computers still don't understand simple language structures, not to mention ambiguity, sarcasm, subtleties, etc.
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1$\begingroup$ That's a very good example. Perception in general is easy for humans but so hard for computers. Vision for example.. $\endgroup$– mrkCommented Feb 18, 2013 at 23:12
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Facial recognition. Human does better and quicker here than computers.
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2$\begingroup$ It is not proven that computers cannot do facial recognition better than humans. The fact that we don't yet know how humans recognize faces doesn't mean that it cannot be implemented on a computer. $\endgroup$– ShaullCommented Feb 18, 2013 at 16:13
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1$\begingroup$ @Shaull It is not proven that computers can do better either. $\endgroup$– mrkCommented Feb 18, 2013 at 23:14
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$\begingroup$ @saadtaame: by the same logic you could argue that $P\neq NP$ because there is no polynomial time algorithm for $SAT$ today. If you claim that facial recognition is something humans will always do better than computers, you need to prove this in general. Claiming that this is not true, however, requires nothing :) $\endgroup$– ShaullCommented Feb 19, 2013 at 17:03
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If you consider computability, human brain is not stronger than Turing machine. Turing machine could have infinite memory (arbitrarily extendable tape) while our memory is not (limit in storing information).
But in some current applications it seems human brain works better according to performance than current computers like Natural language learning, Image/Voice recognition,...
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1$\begingroup$ It is not "fair" to compare the brain to an infinite memory-TM, since any practical TM will have a finite memory. The interesting fact is that as far as we know, even under the restriction of finite memory, the brain is not stronger. $\endgroup$– ShaullCommented Feb 19, 2013 at 6:43
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$\begingroup$ @Shaull: As I mentioned considering computability (from theory). The comparison could be meaningful if you could exactly describe the limitation of two computing machines. If you consider infinite memory for human, it is still not stronger than Turing machine (based on Church-Turing thesis). $\endgroup$– RezaCommented Feb 19, 2013 at 16:49
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$\begingroup$ Exactly. So why answer with a weaker claim? I would say it makes more sense to consider a TM with finite (say, polynomial in the input) memory, rather than considering an infinite-memory brain. But anyway - I agree with what you said, just pointing out you could have said something stronger. $\endgroup$– ShaullCommented Feb 19, 2013 at 16:59
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$\begingroup$ Human brain are reproduced by a Turing machine? So human brain are controlled only by computable functions? Remember that human brain are build by nature, and nature has non-computable functions! $\endgroup$– NogueiraCommented Apr 29, 2015 at 5:22
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$\begingroup$ How do we know the human brain is not stronger than a Turing Machine with finite memory? Computers are only capable of doing a very small portion of our everyday lives, so prima facie seems the brain is much stronger. $\endgroup$– ytersCommented Apr 8, 2017 at 19:32
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Von Neumann suggested his famous computer architecture as a way to simulate the laws of (classical) physics. Furthermore, it was shown that these laws can be simulated efficiently.
If you believe that the human brain works under the constraints of classical physics (also, to an extent, under quantum physics), then the brain is no stronger than a Turing Machine.
In this sense - no, the brain cannot do anything that a computer can't.
You may want to read this.
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$\begingroup$ Are there experiments one way or another that provide evidence whether the human brain works under the constraints of classical/quantum physics, or is this just assumed? $\endgroup$– ytersCommented Apr 8, 2017 at 19:33